🚀 go-pugleaf

In article <1992Dec16.095858.5370@dutrun2.tudelft.nl>, rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:
|> In article <1992Dec15.092610@roper.mc.ti.com> W. Donald Rolph:
|> > You are indeed confused.
|> 
|> I am never confused about these things.
|> 
|> >  Any approximation procedure must have trial functions.
|> 
|> No, no.
|> 
|> > In traditional FEA they are called shape functions, choose the name you like
|> > but all FEA procedures must have some approximating function over the domain
|> > space.
|> 
|> *All* procedures?
|> 
|> Gee, how then could I calculate the temperature distribution in a sodium pump
|> by an direct FE method, WITHOUT ever needing such "approximating functions"?
|> (An accompanying article is called "Multimode Heat Transfer in Sodium Pumps".
|> It is found in the Proceedings of the 0Xth Conference on Numerical Methods
|> in Thermal, or whatever, Problems, Swansea U.K., 197X. Look it up ;-)
|> 
|> I also did some work on pure advection without shape functions. But who am I?
|> There exists CFD code named "FLOTRAN", which has a "streamline upwind" scheme
|> in it, derived directly without shape functions. It's all in my SUNA articles.
|> 
|> And almost any Finite Element book starts with the assembly of resistor-like
|> elements, without approximations. The element-matrix of an electrical resistor
|> is derived directly by applying the laws of Ohm and Kirchhoff, giving:
|> 
|>          | +1/R  -1/R |
|>          | -1/R  +1/R |
|> 
|> Just define the connectivity (no coordinates) of your resistor-network,
|> two voltages as a boundary condition, and go ...
|> -- 
|> * Han de Bruijn; Applications&Graphics | "A little bit of Physics * No
|> * TUD Computing Centre; P.O. Box 354   | would be NO idleness in  * Oil
|> * 2600 AJ  Delft; The Netherlands.     | Mathematics" (HdB).      * for
|> * E-mail: Han.deBruijn@RC.TUDelft.NL --| Fax: +31 15 78 37 87 ----* Blood

When you defined your resistor network you assumed a trial function which is
linear between the nodes.  You also incidentally also assumed triangular elements
if you applied this over 2D surfaces (I assume tetrahedrals over 3D but I haven't
worked that problem out.).  In short just because you chose lumped elements did
not remove you from choosing a trial function, it just hid the trial function
from your observations!  Good luck I enjoy talking with you!!
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263

In article <1992Dec16.095858.5370@dutrun2.tudelft.nl> rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:
>
>Gee, how then could I calculate the temperature distribution in a sodium pump
>by an direct FE method, WITHOUT ever needing such "approximating functions"?
>(An accompanying article is called "Multimode Heat Transfer in Sodium Pumps".

A much better method for this type of heat problem is to use the Transmission
Line Matrix method (TLM) - W.J.R. Hoefer "Huygens and the Computer",
Proc. IEEE, vol. 79, no. 11, October 1991.

I'd be very interested to hear from anyone else who is working with TLM,
please do email me, it might be useful to have some sort of discussion forum.

Regards

Andy

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